Question: A circle with circumference ${18}$ has an arc with a $120^\circ$ central angle. What is the length of the arc?
Answer: The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{120}^\circ}{360^\circ} = \dfrac{{s}}{{{18}}}$ $\dfrac{1}{3} = \dfrac{{s}}{{18}}$ $\dfrac{1}{3} \times {18} = {s}$ $6 = {s}$ ${18}$ ${120^\circ}$ ${6}$